Theorems of Pappus and Pascal and Cubic Curves
Theorems of Pappus and Pascal are concerned with special configurations of lines. They precede the subject of Projective Geometry. We will otline their proofs using the method of transformations, and then proceed to prove a theorem about lines intersecting on a cubic, that generalises Pascal's and Pappus' Theorems. We shal also present a more "classical" proof of Pappus' Theorem using the concept of cross-ratio.